Question

如图,在△ABC中,BP平分∠CAP,CP平分∠ACD,试探究∠A与∠BPC的关系?

Answer 1

∵ BP平分∠ABC CP平分∠ACD

∴ ∠PBC=1/2∠ABC ∠PCD=1/2∠ACD

又 ∵ ∠ACD=∠A+∠ABC 即∠A=∠ACD－∠ABC

同理∠P=∠PCD－∠PBC

∴ ∠BPC=1/2∠ACD-1/2∠ABC=1/2(∠ACD-∠ABC)=1/2∠A

即∠BPC=1/2∠A